In a transmission electron microscope, an electron beam is directed at the object to be analyzed and then depicted by way of electromagnetic lenses after traversing the object. In a manner similar to lenses for visible light, electromagnetic lenses for diffracting electrons have image defects, and these image defects can degrade the resolution capacity of the microscope. Such image defects are referred to as aberrations. In conventional electromagnetic circular lenses, so-called spherical aberration is by far the strongest image defect. In addition to spherical aberration, a variety of other aberrations exist, which can be categorized based on different mathematical systems. For example, in addition to defocusing and astigmatism, which in ophthalmology are equivalent to the terms near-sighted/far-sighted and astigmatism of the eye, many other types of aberration occur, such as axial coma, third-, fourth-, fifth-, and sixth-order astigmatism, star aberration, three leaf clover aberration, and many more. The number and/or order of the aberrations, which play a significant role in a transmission electron microscope with respect to the imaging quality, climb with the increasing resolution capacity of the microscope. The knowledge and/or the correction of aberrations plays a crucial role in the modern transmission electron microscope, the resolution capacity of which is only slightly greater than, or even less than, 0.1 nanometers.
In order to be able to determine aberrations of a transmission electron microscope, the tilted tableau, or Zemlin tableau, method (F. Zemlin et al., “Coma-free alignment of high resolution electron microscopes with the aid of optical diffractograms”, Ultramicroscopy 3, 49-60 (1978)) is generally employed. For this purpose, images of a thin amorphous object site are recorded under different tilt angles of the incident electron beam, and the effective defocusing and effectively present astigmatism are determined for each individual image of the tilt series. Effectively present defocusing and astigmatism, as the lowest order aberrations, are induced by the higher order aberrations, and thus it is possible to determine the desired unknown aberrations of a higher order from the defocusing and astigmatism values from the tilt series.
While, in the case of conventional electron microscopes, which exclusively comprise electromagnetic circular lenses, it is possible to determine a variety of aberrations using the tilted tableau method described above, the correctable aberrations are limited to defocusing, second- and third-order astigmatism, and axial coma. In particular, while the strongly dominating spherical aberration can be determined in a microscope fitted with circular lenses, it cannot be corrected.
In order to increase the resolution capacity, an electron microscope having a corrector for spherical aberration is known from (S. Uhlemann, M. Haider: “Residual wave aberrations in the first spherical aberration corrected transmission electron microscope”, Ultramicroscopy 72, 109-119 (1998)). In addition to circular lenses, this corrector comprises two electromagnetic hexapoles, which allow for the compensation of the spherical aberration. In order to even be able to adjust and use the corrector in the desired manner, which in turn may unintentionally create a variety of additional aberrations, the aberrations that are still unknown are first determined, likewise using the tilted tableau method. Thereafter, in particular the spherical aberration determined in this way, and several other aberrations, can be compensated for through proper adjustment of the hardware corrector as early as during the imaging process. Once again, the determination of aberrations by means of defocusing and astigmatism measurements plays a crucial role.
In order to determine defocusing and astigmatism in an experimentally recorded image of a thin amorphous object site, a Fourier space representation of the same is created. This Fourier space representation, which is also referred to as a diffractogram, has a stripe pattern that is typical of the respective defocusing and astigmatism. The goal is to quantitatively pick up the stripe pattern and to be able to assign defocusing and astigmatism values to it clearly and with maximum precision.
For the detection of the stripe pattern, a variety of possible diffractograms are computed, which differ with respect to defocusing and astigmatism. These computed diffractograms are then compared, either visually by eye, or by machine, to the experimentally obtained diffractogram in order to determine the defocusing and astigmatism values actually present in the experiment based on maximum similarity between the experimental and simulated stripe patterns. A reference to machine-based pattern detection can be found in (A. Thust et al., “Numerical correction of lens aberrations in phase-retrieval HRTEM”, Ultramicroscopy 64, 249-264 (1996)) and in (S. Uhlemann, M. Haider: “Residual wave aberrations in the first spherical aberration corrected transmission electron microscope”, Ultramicroscopy 72, 109-119 (1998)), but the cited references do not in any way address the special algorithmic implementation of pattern detection. Visual pattern detection by eye is described in (Johannes Zemlin, Friedrich Zemlin “Diffractogram tableaux by mouse click”, Ultramicroscopy 93 77-82, (2002)). The latter visual method of pattern detection is not suited for practical, daily use, due to the slow speed and subjective nature of the human comparison of patterns, so that only the machine-based comparison of patterns remains as a proven means for determining defocusing and astigmatism values in order to determine microscope aberrations.
The comparison of an experimental diffractogram to simulated diffractograms according to the state of the art is highly error-prone and imprecise, since the experimentally measured diffractogram is superimposed both with strong additive and multiplicative interferences, the intensity of which can by far exceed that of the useful signal. The separation of strong additive and multiplicative interferences that are difficult to quantify from the actual useful signal is a challenge, which up to now has not been satisfactorily resolved. First, there is the risk that the useful signal is not even detected against the background interference, which is to say that the interfering signal is interpreted as a useful signal, which can produce a completely incorrect result and/or result in a breakdown of the stripe detection process. Secondly, there is the risk that even if the separation of the interfering and useful signals is successful in principle, the result of the defocusing and astigmatism determination does not satisfy the quantitative accuracy requirements. In the first case, it is not possible to adjust the microscope aberrations, and in the latter case, while the microscope can be roughly adjusted, the residual aberrations still present due to the imprecise measurement do not allow for optimum utilization of the performance capability of the microscope.